What is the integral from 1 to 2 of xsin(x) ?

The integral from 1 to 2 of xsin(x) is -2cos(2)+sin(2)+cos(1)-sin(1)

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integral from 1 to 2 of xsin(x)

\int_{1}^{2} x sin (x) d x

- 2 cos (2) + sin (2) + cos (1) - sin (1)

Decimal

1.44042 \dots

Solution steps

\int_{1}^{2} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{1}^{2}

= [- x cos (x) - \int - cos (x) d x]_{1}^{2}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{1}^{2}

Simplify

= [- x cos (x) + sin (x)]_{1}^{2}

Compute the boundaries:

- 2 cos (2) + sin (2) + cos (1) - sin (1)

= - 2 cos (2) + sin (2) + cos (1) - sin (1)

\int_{0}^{12} 2 x d x

\int_{- 1}^{2} e^{x^{2}} d x

\int_{0}^{a} 2 x d x

\int_{2}^{7} e^{2 - x} d x

\int_{- 3}^{3} x x^{4} + 1 d x

What is the integral from 1 to 2 of xsin(x) ?
The integral from 1 to 2 of xsin(x) is -2cos(2)+sin(2)+cos(1)-sin(1)